4.2 Standard Form of a Quadratic Function The standard form of a quadratic function is f(x) = ax² + bx + c, where a ≠ 0. For any quadratic function f(x)

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Presentation transcript:

4.2 Standard Form of a Quadratic Function The standard form of a quadratic function is f(x) = ax² + bx + c, where a ≠ 0. For any quadratic function f(x) = ax² + bx + c, the values of a, b, and c provide key information about its graph. – Can find information about the graph of a quadratic function (such as the vertex) from the vertex form. – Standard form is easier to enter into a graphing calculator.

Finding the Features of a Quadratic Function What are the vertex, the axis of symmetry, the maximum or minimum value, and the range of y = 2x² + 8x – 2 ?

Finding the Features of a Quadratic Function What are the vertex, the axis of symmetry, the maximum or minimum value, and the range of y = 2x² + 8x – 2 ? Range: y ≥ -10 Vertex: (-2, -10) Axis of symmetry: x = -2 Minimum value: -10

Graphing a Function of the Form y = ax 2 + bx + c What is the graph of y = x 2 + 2x + 3? a = 1, b = 2, c = 3 axis of symmetry: Vertex: y = (-1)² + 2(-1) + 3 = 2 (-1, 2)

Converting Standard Form to Vertex Form What is the vertex form of y = 2x² + 10x + 7?

More Practice!!!!! Homework – Textbook p. 206 #8 – 31.